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Elliptic Subfields and Automorphisms of Genus 2 Function Fields

In: Algebra, Arithmetic and Geometry with Applications

Author

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  • Tanush Shaska
  • Helmut Völklein

Abstract

We study genus 2 function fields with elliptic subfields of degree 2. The locus ℒ2 of these fields is a 2-dimensional subvariety of the moduli space M 2 of genus 2 fields. An equation for ℒ2 is already in the work of Clebsch and Bolza. We use a birational parameterization of ℒ2 by affine 2-space to study the relation between the j-invariants of the degree 2 elliptic subfields. This extends work of Geyer, Gaudry, Stichtenoth and others. We find a 1-dimensional family of genus 2 curves having exactly two isomorphic elliptic subfields of degree 2; this family is parameterized by the j-invariant of these subfields.

Suggested Citation

  • Tanush Shaska & Helmut Völklein, 2004. "Elliptic Subfields and Automorphisms of Genus 2 Function Fields," Springer Books, in: Chris Christensen & Avinash Sathaye & Ganesh Sundaram & Chandrajit Bajaj (ed.), Algebra, Arithmetic and Geometry with Applications, pages 703-723, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18487-1_42
    DOI: 10.1007/978-3-642-18487-1_42
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